f(x)=-√3sin^2x+sinxcosx =-√3(1-cos2x)/2+sin2x/2=sin2x/2+√3cos2x/2-√3/2=sin(2x+π/3)-√3/2因为X∈[0,π/2],所以2x+π/3∈[π/3,4π/3]所以sin(2x+π/3)∈[-√3/2,1]所以f(x)∈[-√3,1-√3/2]...